For graphics development, I primarily use Adobe Photoshop 3.0. It's probably the most powerful graphics tool I've used. Photoshop does have some deficiencies, however. Things like the drawing of a simple circle are remarkably over-complex actions in Photoshop. That's probably what Adobe made Illustrator for.
To compensate for some of these deficiencies, I've also used Microsoft Image Composer in conjunction with Photoshop for some graphics development. Image Composer has some rather nice features, including sprite alignment tools.
I'm still debating the upgrade to Photoshop 4.0 and the purchase of Illustrator, so if you have any recommendations, or if you have any questions or comments regarding anything on my site, please mail me.
For HTML authoring, however, I used no fancy software beyond a text editor such as emacs or Programmer's File Editor (a nice text editor for Windows, by the way). While coding these pages by hand may get slightly tedious, I maintain control over the presentation of pages in all browsers. There's no such thing as a WYSIWYG HTML editor.
For more of my web development work, feel free to browse some of my older pages. I can't guarantee that they'll be kind to your modem (or your eyes) or that they're more exciting than What I Did This Summer, but you can see the evolution of my homesite.